Gravito-electromagnetism

TL;DR

This paper develops a covariant 1+3 formalism for gravity, establishing a detailed analogy with electromagnetism through tensor fields, and explores invariance and conservation properties of gravitational energy and duality.

Contribution

It introduces a covariant electromagnetic analogy for gravity using tensor fields, extending the formalism and invariance properties of gravitational equations.

Findings

Covariant analogy between Bianchi and Maxwell equations.

Identification of gravitational sources and potentials with electromagnetic analogues.

Construction of super-energy density and conservation equations.

Abstract

We develop and apply a fully covariant 1+3 electromagnetic analogy for gravity. The free gravitational field is covariantly characterized by the Weyl gravito-electric and gravito-magnetic spatial tensor fields, whose dynamical equations are the Bianchi identities. Using a covariant generalization of spatial vector algebra and calculus to spatial tensor fields, we exhibit the covariant analogy between the tensor Bianchi equations and the vector Maxwell equations. We identify gravitational source terms, couplings and potentials with and without electromagnetic analogues. The nonlinear vacuum Bianchi equations are shown to be invariant under covariant spatial duality rotation of the gravito-electric and gravito-magnetic tensor fields. We construct the super-energy density and super-Poynting vector of the gravitational field as natural U(1) group invariants, and derive their super-energy conservation equation. A covariant approach to gravito-electric/magnetic monopoles is also presented.